Sorry. But whatever you did in Excel is apparently flat out wrong. Lets just think about this, for a moment. Does it make even remote sense that the curve should be a decreasing function, thus a negative slope? You do say that is the result you got when you solved it on paper, and in Excel, did you not?
We see that t runs from 0-90, so ALWAYS non-negative t.
Then we see dy/dt, computed as:
a = 30;
Ddv_Div = t*exp(-t^2/(2*a^2));
t is positive, and exp(anything real) is a positive number. The product of two positive real numbers is, well also positive.
So the derivative of the function is ALWAYS positive for positive t.
Is it possible to have a function to have a negative slope, yet ALWAYS a positive first derivative over that interval? Yeah, right.
So I have no idea what you solved on paper, but you got something wrong when you did it yourself, and when you used Excel. At least, in comparison to what you solved in MATLAB. The mathematics cannot lie. Either the derivative you provided is simply wrong, or you made a big mistake when you solved it yourself. What I cannot do is check your solution, since we have not been given the equations you are trying to solve, nor have we been told what you did on paper. I do know that something you have done is incorrect, and MATLAB did not do the wrong thing with what you gave it.